Denoising Various ECG Artifacts By Multi Rate Filter Bank and Wavelet Thresholding

81 Pages·2017·1.24 MB·English

by  Seung Man Kim

DENOISING VARIOUS ECG ARTIFACTS BY MULTI RATE FILTER BANK

AND WAVELET THRESHOLDING

A Thesis

Presented to the

Faculty of

California State Polytechnic University, Pomona

In Partial Fulfillment

Of the Requirements for the Degree

Master of Science

In

Electrical Engineering

By

Seung Man Kim

2017
SIGNATURE PAGE
THESIS: DENOISING VARIOUS ECG
ARTIFACTS BY MULTI RATE FILTER
BANK AND WAVELET
THRESHOLDING

AUTHOR: Seung Man Kim

DATE SUBMITTED: Winter 2017

Electrical and Computer Engineering Department

Dr. James Kang
Thesis Committee Chair
Electrical and Computer
Engineering

Dr. Thomas Ketseoglu
Electrical and Computer
Engineering

Dr. Salomon Oldak
Electrical and Computer
Engineering

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ACKNOWLEDGEMENTS

First of all, I sincerely appreciate my advisor Dr. James Kang for his continuous
help and support. With his great consulting, I always was able to come up some new
ideas or direction to solve problems related my research. Without his influence, I couldn't
even have accomplished this much.

In addition, I would like to thank the all ECE faculty who have taught me a lot of
great knowledge. With the wisdom from all other professors, I was able to build up from
very fundamental concept, such as filter, sampling, orthogonality, subspace and
stochastic processing topics which are important in order to be able to understand my
research method.

Many thanks to Hyunyoul Seo, President at Bionet America, Inc, who was always
supporting and allowing me to access ECG data for this research. Furthermore, I would
like to thank Eugene Palatnik at ITEC Engineering LLC who provide me real rat's ECG
data for this thesis.

Lastly I sincerely thank my wife and two daughters for all their support, and love.
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ABSTRACT

The electrocardiogram (ECG) is a time varying signal and it is used to diagnose
various cardiovascular diseases or evaluate patient's condition. Normally, the ECG's
characteristic points, P, Q, R, S, and T are used in diagnosis. An example where a
patient’s heart rate is a valuable piece of information would be in an operation room
where the anesthesiologist is preparing to put the patient to sleep. This ECG signal can be
corrupted in many different ways such as white noise from patient's skin condition, from
electrodes that do not have a proper connection, muscle contractions, baseline wandering
caused by the patient breathing, and power noise.
In this study, various ECGs signals such as synthetic ECG with white noise, real
human ECG with Electromyogram (EMG) noise, and an a rat's ECG for power noise will
be denoised by multi rate filter bank with Coif5 wavelet and both soft and hard
thresholding. For this research paper, all the proposed filters and algorithms will be
developed and tested using Matlab.
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TABLE OF CONTENTS

SIGNATURE PAGE .......................................................................................................... ii

ACKNOWLEDGEMENTS ............................................................................................... iii

ABSTRACT ....................................................................................................................... iv

LIST OF TABLE ............................................................................................................... vi

LIST OF FIGURES .......................................................................................................... vii

Chapter 1 Introduction ........................................................................................................ 1

Chapter 2 Wavelet Transform ............................................................................................. 4

Comparison between different transforms ................................................................................. 11

Uncertainty Principle ................................................................................................................. 13

Chapter 3 Multirate filter bank ......................................................................................... 15

Denoising ................................................................................................................................... 23

Chapter 4 Denoising white Gaussian noise ...................................................................... 26

Chapter 5 Human ECG with muscle noise ....................................................................... 49

Chapter 6 Power noise removal from rat's ECG ............................................................... 55

Chapter 7 Conclusion........................................................................................................ 64

Chapter 8 Future research opportunity ............................................................................. 66

REFERENCES ................................................................................................................. 68

APPENDIX A ................................................................................................................... 70

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LIST OF TABLE

Table 1-Result of denoising synthetic ECG...................................................................... 64

Table 2-Daubechies2 Coefficient, p=2 ............................................................................. 70

Table 3-Daubechies 4 Coefficient, p=4 ............................................................................ 70

Table 4-Coiflets 5 Coefficient, p=5 .................................................................................. 70

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LIST OF FIGURES

Figure 1.1: ECG waveform with characteristic point ......................................................... 2

Figure 2.1: Haar Wavelet .................................................................................................... 5

Figure 2.2: Scaled basis ϕ_n (t) from Chun-Lin, Liu .......................................................... 9

Figure 2.3: Different time-frequency tile resolution of the three transforms a) Fourier

Transform, b) STFT, and c) Wavelet Transform from Chun-Liu..................................... 12

Figure 3.1: Relationship diagram between scaling function and wavelet function space 17

Figure 3.2: The relationship between scaling and wavelet functions from Chun-Lin. .... 17

Figure 3.3: Two Channel Filter Bank ............................................................................... 19

Figure 3.4: Three Level Filter Bank, Mallat's algorithm .................................................. 20

Figure 3.5: Spectrum of LPF and HPF in Three Level Filter Bank .................................. 21

Figure 3.6: Frequency response of different wavelet filter bank ...................................... 22

Figure 3.7: Band Pass Frequency Spectrum of HPF (Wavelet function) in Mallat's

algorithm (non ideal case) ................................................................................................. 22

Figure 3.8: Band width of each level decomposition of Mallat algorithm ) is output of

LPF and < is output of HPF ........................................................................................... 23

Figure 3.9: Thresholding a) hard threshoding , b) Soft thresholding from M. Steinbuch

and M.J.G. van de Molengraft .......................................................................................... 24

Figure 4.1: Detail Coefficient with random noise V=0.01 ................................................ 27

Figure 4.2: Approximation Coefficient with random noise V=0.01 ................................. 28

Figure 4.3: Filter input vs. Filter output with random noise V=0.01 ................................ 29

Figure 4.4: No noise ECG vs. Filter ECG with random noise V=0.01........................... 30

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Figure 4.5: Approximation coefficient with baseline wandering with random noise
V=0.01 ............................................................................................................................... 31

Figure 4.6: Filter Bank Input vs. Filter Bank Output with random noise V=0.01. ........... 32

Figure 4.7: Original ECG vs. Filter Output without DC offset adjusted with random noise

V=0.01. .............................................................................................................................. 33

Figure 4.8: Original ECG vs. Filter Output after DC offset applied with random noise

V=0.01 ............................................................................................................................... 34

Figure 4.9: Detail Coefficient with random noise V=0.1 .................................................. 35

Figure 4.10: Approximation Coefficient with random noise V=0.1 ................................. 36

Figure 4.11: Filter Bank Input vs. Filter Bank Output with random noise V=0.1 ........... 37

Figure 4.12: No noise ECG vs. Filter ECG with random noise V=0.1 ............................. 38

Figure 4.13: Details of No noise ECG vs. Filter ECG with random noise V=0.1 ............ 38

Figure 4.14: Approximation Coefficient with random noise V=0.1 and baseline

wandering .......................................................................................................................... 39

Figure 4.15: Filter Bank Input vs. Filter Bank Output with random noise V=0.1 and

baseline noise .................................................................................................................... 40

Figure 4.16: Original ECG vs. Filter Output without adjusting DC offset with random

noise V=0.01 and baseline. ............................................................................................. 41

Figure 4.17: Original ECG vs. Filter Output after adjusting DC offset with random noise

V=0.01 and baseline. ......................................................................................................... 42

Figure 4.18: Details of Original ECG vs. Filter Output after adjusting DC offset with

random noise V=0.01 and baseline. .................................................................................. 43

Figure 4.19: Input signal with random noise, V=0.5......................................................... 44

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Figure 4.20: Detail Coefficient with random noise V=0.5 ................................................ 45

Figure 4.21: Detail Coefficient with random noise V=0.5 ................................................ 46

Figure 4.22: Filter Bank Input vs. Filter Bank Output with random noise V=0.5 ............ 46

Figure 4.23: Original ECG vs. Filter Output without adjusting DC offset with V=0.5 . 47

Figure 4.24: Details of Original ECG vs. Filter Output with random noise V=0.5 .......... 48

Figure 5.1: Measured patient ECG signal (Lead II ) ........................................................ 49

Figure 5.2: Detail coefficient of level 9 MRA filter bank ................................................ 50

Figure 5.3: Approximation coefficient of level 9 MRA filter bank .................................. 51

Figure 5.4: Original Signal vs. Filter Signal ..................................................................... 52

Figure 5.5: Zoomed in high frequency muscle noise part ................................................ 53

Figure 5.6: Zoomed in low frequency muscle noise part.................................................. 54

Figure 6.1: Power noise spectrum with its harmonics ...................................................... 55

Figure 6.2: Filtered power noise spectrum. ...................................................................... 56

Figure 6.3: Input vs. Output of notch filter ....................................................................... 57

Figure 6.4: Details of the filtered signal ........................................................................... 58

Figure 6.5: Detail coefficient of MRA filter bank with hard thresholding ....................... 58

Figure 6.6: Approximation coefficient of MRA filter bank with hard thresholding ........ 59

Figure 6.7: Input vs. Output of MRA filter bank and hard thresholding .......................... 60

Figure 6.8: Details of Input vs. Output of MRA filter bank and hard thresholding ......... 60

Figure 6.9: Input vs. Output of MRA filter bank and Soft Thresholding ......................... 61

Figure 6.10: Details of Input vs. Output of MRA filter bank and Soft thresholding ........ 62

Figure 6.11: Spectrum of filtered signal by MRA filter bank with hard thresholding ..... 63

Figure 6.12: Spectrum of filtered signal by MRA filter bank with Soft thresholding ...... 63

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Figure 8.1: Coif5 Scaling and Wavelet function .............................................................. 66

Figure 8.2: PVC ECG waveform ...................................................................................... 67

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